Pleasant extensions retaining algebraic structure, II

Tim Austin

Research output: Contribution to journalArticle

Abstract

In this paper, we combine the general tools developed in [5] with several ideas taken from earlier work on one-dimensional nonconventional ergodic averages by Furstenberg and Weiss [17], Host and Kra [21] and Ziegler [44] to study the averages (Formula presented.) associated to a triple of directions p<inf>1</inf>, p<inf>2</inf>, p<inf>3</inf> ∈ ℤ<sup>2</sup> that lie in general position along with 0 ∈ ℤ<sup>2</sup>. We show how to construct a “pleasant” extension of an initiallygiven ℤ<sup>2</sup>-system for which these averages admit characteristic factors with a very concrete description, involving the same structure as for those in [2] together with two-step pro-nilsystems (reminiscent of [21] and its predecessors). We also use this analysis to construct pleasant extensions and then prove norm convergence for the polynomial nonconventional ergodic averages (Formula presented.) associated to two commuting transformations T<inf>1</inf>, T<inf>2</inf>.

Original languageEnglish (US)
JournalJournal d'Analyse Mathematique
Volume126
Issue number1
DOIs
StatePublished - Apr 20 2015

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Ergodic Averages
Algebraic Structure
Norm
Polynomial

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

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Pleasant extensions retaining algebraic structure, II. / Austin, Tim.

In: Journal d'Analyse Mathematique, Vol. 126, No. 1, 20.04.2015.

Research output: Contribution to journalArticle

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